The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

Question

The probability of rain in Greg’s town on Tuesday is 0.3. The probability that Greg’s teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other. What is the probability that either or both events occur ?

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

A. 0.28
B. 0.32
C. 0.44
D. 0.56
E. 0.6

sahuanamika · Answer

Let's say A event - raining so, P(A) = 0.3 
B event - Quiz so , P(B) = 0.2

P(A and B) = P(A)* P(B) as both are independent = 0.3*0.2 = 0.06
P(A or B) = P(A) + P(B) - P(A and B) 
P(A) = 0.3+0.2 - 0.06 = 0.44 
Ans C

Kinshook · Answer

Given: The probability of rain in Greg’s town on Tuesday is 0.3. The probability that Greg’s teacher will give him a pop quiz on Tuesday is 0.2. The events occur independently of each other.

Asked: What is the probability that either or both events occur ?

Event A: Rain in Greg’s town on Tuesday
Event B: Greg’s teacher will give him a pop quiz on Tuesday

P(A) = .3
P(B) = .2
P(A&B) = .3*.2 = .06
P(AUB) = .3 + .2 - .06 = .44

IMO C

unraveled · Answer

The most important part of the question is that the two events are independent. Thus, probability of them occurring together must be subtracted form the total of independent occurrence. 
P = 0.3+0.2 - 0.3*0.2 = 0.44

Answer C.

singhaz · Answer

What is the probability that  either or both events occur  ?
The question stem ask either or both means P(A∪B) & P(A∩B) which gives ans 0.56

The symbol "∪" (union) means "or". i.e., P(A∪B) is the probability of happening of the event A or B. To find, P(A∪B), we have to count the sample points that are present in both A and B. So is P(A∪B) = P(A) + P(B)? No, because while counting the sample points from A and B, the sample points that are in A∩B are counted twice. Thus, we need to subtract P(A∩B) from the above sum to get P(A∪B).
 Bunuel

Adarsh_24 · Answer

Can we do 1-neither = 1-(.7 * .8) = .44 ?
My doubt is regarding multiplying probability of events not happening is possible if both events are independent.

I think it can. Since, in a vennn diagram it will be the intersection of outside A and outside B => Outside of both.

luisdicampo · Answer

Deconstructing the Question

We want the probability that  either or both  events occur.

Let  A  be the event that it rains on Tuesday, and let  B  be the event that Greg gets a pop quiz on Tuesday.

The key idea is to use the union formula:

P(A\cup B)=P(A)+P(B)-P(A\cap B)

Since the events are  independent , we can compute the overlap using multiplication.

Step-by-step

Let:

P(A)=0.3

and

P(B)=0.2

Because the events are independent:

P(A\cap B)=P(A)\cdot P(B)=0.3\cdot 0.2=0.06

Now apply the union formula:

P(A\cup B)=P(A)+P(B)-P(A\cap B)

=0.3+0.2-0.06

=0.44

So the probability that either or both events occur is  0.44 .

Answer: C) 0.44

The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

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The probability of rain in Greg’s town on Tuesday is 0.3. The probabil

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